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Hook-content Formulae for Symplectic and Orthogonal Tableaux
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- Journal:
- Canadian Mathematical Bulletin / Volume 55 / Issue 3 / 01 September 2012
- Published online by Cambridge University Press:
- 20 November 2018, pp. 462-473
- Print publication:
- 01 September 2012
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- Article
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By considering the specialisation
${{s}_{\lambda }}(1,\,q,\,{{q}^{2}},\ldots ,\,{{q}^{n-1}})$ of the Schur function, Stanley was able to describe a formula for the number of semistandard Young tableaux of shape 
$\lambda $ in terms of the contents and hook lengths of the boxes in the Young diagram. Using specialisations of symplectic and orthogonal Schur functions, we derive corresponding formulae, first given by El Samra and King, for the number of semistandard symplectic and orthogonal $\lambda $-tableaux.
